On 11/15/05, Joseph Wang <[hidden email]>
wrote:
> Here is a silly question. Why is it that LMM methods are
used only with
> Monte Carlo and not with finite difference
methods.
LMM are intrinsically high-dimension. If you model the 30-year
yield
curve as a strip of 6-month forward libor you have 60 factors. FD
with
more than 3 factors are less efficient than MC, and very hard
(almost
impossible?) to implement.
> I'm probably
> missing
something very fundamental, but it seems mathematically possible
> to
write a FDM engine that calculates the forward curve.
Many banks do not
actually evolve 60 factors, but use factor analysis
(PCA) to reduce
dimensionality and evolve just 2 or 3 main factors. It
might be possible to
use FD for such a reduced version of LMM and a FD
implementation of
reduced-dimension LMM would be great as it could
easily account for American
exercise.
The lack of literature on this topic suggests me that a) it must
be
undisclosed proprietary leading edge stuff, or that b)
implementation
details (i.e. boundary conditions) must be so complex to make
the
implementation unfeasible
ciao --
Nando
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